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Simplifying 5x2 + -12x + -91 = 0 Reorder the terms: -91 + -12x + 5x2 = 0 Solving -91 + -12x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -18.2 + -2.4x + x2 = 0 Move the constant term to the right: Add '18.2' to each side of the equation. -18.2 + -2.4x + 18.2 + x2 = 0 + 18.2 Reorder the terms: -18.2 + 18.2 + -2.4x + x2 = 0 + 18.2 Combine like terms: -18.2 + 18.2 = 0.0 0.0 + -2.4x + x2 = 0 + 18.2 -2.4x + x2 = 0 + 18.2 Combine like terms: 0 + 18.2 = 18.2 -2.4x + x2 = 18.2 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 18.2 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 18.2 + 1.44 Combine like terms: 18.2 + 1.44 = 19.64 1.44 + -2.4x + x2 = 19.64 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 19.64 Calculate the square root of the right side: 4.431703961 Break this problem into two subproblems by setting (x + -1.2) equal to 4.431703961 and -4.431703961.Subproblem 1
x + -1.2 = 4.431703961 Simplifying x + -1.2 = 4.431703961 Reorder the terms: -1.2 + x = 4.431703961 Solving -1.2 + x = 4.431703961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 4.431703961 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 4.431703961 + 1.2 x = 4.431703961 + 1.2 Combine like terms: 4.431703961 + 1.2 = 5.631703961 x = 5.631703961 Simplifying x = 5.631703961Subproblem 2
x + -1.2 = -4.431703961 Simplifying x + -1.2 = -4.431703961 Reorder the terms: -1.2 + x = -4.431703961 Solving -1.2 + x = -4.431703961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -4.431703961 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -4.431703961 + 1.2 x = -4.431703961 + 1.2 Combine like terms: -4.431703961 + 1.2 = -3.231703961 x = -3.231703961 Simplifying x = -3.231703961Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.631703961, -3.231703961}
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